Estimating the Mode Shapes of a Bridge Using Short Time Transmissibility Measurement from a Passing Vehicle

Document Type : Research Paper

Authors

1 PhD Student, Faculty of Mechanical Engineering, Babol University of Technology Shariati Av., Babol, 47148-71167, Iran

2 Associate Professor, Faculty of Mechanical Engineering, Babol University of Technology, Shariati Av., Babol, 47148-71167, Iran

3 Assistant Professor, Faculty of Mechanical Engineering, Semnan University, Central Administration of Semnan University, Campus 1, Semnan, 35131-19111, Iran

Abstract

This paper reports on the analysis of the signals sent by accelerometers fixed on the axles of a vehicle which passes over a bridge. The length of the bridge is divided into some parts and the transmissibility measurement is applied to the signals recorded by two following instrumented axles. As the transmissibility procedure is performed on the divided signals, the method is called Short Time Transmissibility Measurement. Afterwards, a rescaling process is accomplished in order to estimate the bridge mode shapes. The numerical results indicate that the method can calculate the mode shapes of the bridge accurately. It is demonstrated that short time transmissibility method does not depend on the excitation characteristics contrary to the other related methods which assume that the excitation should be white noise. Generally, the bridge mode shapes may be invisible due to the excitation exerted by the road profile. This issue is also resolved by subtracting the signals from the successive axles. Finally, the signals are contaminated with noise and the robustness of the method is investigated.

Keywords

Main Subjects

[1] Yang, J., Lam, H., Hu, J., Ambient vibration test, modal identification and structural model updating following Bayesian framework. International Journal of Structural Stability and Dynamics, 15(7), 2015, 1540024.
[2] Curadelli, R., et al., Damage detection by means of structural damping identification. Engineering Structures, 30(12), 2008, 3497-3504.
[3] Williams, C., Salawu, O., Damping as a damage indication parameter. in Proceedings of SPIE - The International Society for Optical Engineering. 1997.
[4] Kim, J.-T., et al., Damage identification in beam-type structures: frequency-based method vs mode-shape-based method. Engineering Structures, 25(1), 2003, 57-67.
[5] Ventura, C., Felber, A., Stiemer, S., Determination of the dynamic characteristics of the Colquitz River Bridge by full-scale testing. Canadian Journal of Civil Engineering, 23(2), 1996, 536-548.
[6] Huang, C., et al., Dynamic testing and system identification of a multi‐span highway bridge. Earthquake Engineering & Structural Dynamics, 28(8), 1999, 857-878.
[7] Yang, Y.-B., Lin, C., Yau, J., Extracting bridge frequencies from the dynamic response of a passing vehicle. Journal of Sound and Vibration, 272(3), 2004, 471-493.
[8] Lin, C., Yang, Y., Use of a passing vehicle to scan the fundamental bridge frequencies: An experimental verification. Engineering Structures, 27(13), 2005, 1865-1878.
[9] Oshima, Y., et al. Estimation of bridge eigenfrequencies based on vehicle responses using ICA. in Proceedings of the 10th International Conference on Structural Safety and Reliability (ICOSSAR’09). 2009.
[10] Yang, Y., Chang, K., Extraction of bridge frequencies from the dynamic response of a passing vehicle enhanced by the EMD technique. Journal of Sound and Vibration, 322(4), 2009, 718-739.
[11] Li, W.-m., et al., Optimization method based on Generalized Pattern Search Algorithm to identify bridge parameters indirectly by a passing vehicle. Journal of Sound and Vibration, 333(2), 2014, 364-380.
[12] Malekjafarian, A., O'Brien, E.J., Application of output-only modal method in monitoring of bridges using an instrumented vehicle. in Civil Engineering Research in Ireland, Belfast, UK, 28-29 August, 2014. 2014.
[13] Zhu, X., Law, S., Wavelet-based crack identification of bridge beam from operational deflection time history. International Journal of Solids and Structures, 43(7), 2006, 2299-2317.
[14] Pandey, A., Biswas, M., Samman, M., Damage detection from changes in curvature mode shapes. Journal of Sound and Vibration, 145(2), 1991, 321-332.
[15] Yang, Y., Li, Y., Chang, K., Constructing the mode shapes of a bridge from a passing vehicle: a theoretical study. Smart Structures and Systems, 13(5), 2014, 797-819.
[16] Oshima, Y., Yamamoto, K., Sugiura, K., Damage assessment of a bridge based on mode shapes estimated by responses of passing vehicles. Smart Structures and Systems, 13(5), 2014, 731-753.
[17] Zhang, Y., Wang, L., Xiang, Z., Damage detection by mode shape squares extracted from a passing vehicle. Journal of Sound and Vibration, 331(2), 2012, 291-307.
[18] Oshima, Y., et al. Eigenfrequency estimation for bridges using the response of a passing vehicle with excitation system. in Proceedings of the fourth international conference on bridge maintenance, safety and management. 2008.
[19] Malekjafarian, A., O'Brien, E.J., Identification of bridge mode shapes using short time frequency domain decomposition of the responses measured in a passing vehicle. Engineering Structures, 81, 2014, 386-397.
[20] McGetrick, P.J., Gonzlez, A., OBrien, E.J., Theoretical investigation of the use of a moving vehicle to identify bridge dynamic parameters. Insight-Non-Destructive Testing and Condition Monitoring, 51(8), 2009, 433-438.
[21] Chang, K., Wu, F., Yang, Y., Effect of road surface roughness on indirect approach for measuring bridge frequencies from a passing vehicle. Interaction and Multiscale Mechanics, 3(4), 2010, 299-308.
[22] He, W.-Y., He, J., Ren, W.-X., Damage localization of beam structures using mode shape extracted from moving vehicle response. Measurement, 121, 2018, 276-285.
[23] He, W.Y., Ren, W.X., Zuo, X.H., Mass‐normalized mode shape identification method for bridge structures using parking vehicle‐induced frequency change. Structural Control and Health Monitoring, 25(6), 2018, 2174.
[24] Malekjafarian, A., OBrien, E.J., On the use of a passing vehicle for the estimation of bridge mode shapes. Journal of Sound and Vibration, 397, 2017, 77-91.
[25] Yang, Y., Yang, J.P., State-of-the-art review on modal identification and damage detection of bridges by moving test vehicles. International Journal of Structural Stability and Dynamics, 18(2), 2018, 1850025.
[26] Brincker, R., Zhang, L., Andersen, P., Modal identification of output-only systems using frequency domain decomposition. Smart Materials and Structures, 10(3), 2001, 441.
[27] Devriendt, C., Guillaume, P., The use of transmissibility measurements in output-only modal analysis. Mechanical Systems and Signal Processing, 21(7), 2007, 2689-2696.
[28] Yan, W.J., Ren, W.X., Operational modal parameter identification from power spectrum density transmissibility. Computer‐Aided Civil and Infrastructure Engineering, 27(3), 2012, 202-217.
[29] Kong, X., Cai, C., Kong, B., Damage detection based on transmissibility of a vehicle and bridge coupled system. Journal of Engineering Mechanics, 141(1), 2014, 04014102.
[30] Ewins, D., Modal testing: theory, practice and application (mechanical engineering research studies: engineering dynamics series). 2003.
[31] Araújo, I.G., Laier, J.E., Operational modal analysis using SVD of power spectral density transmissibility matrices. Mechanical Systems and Signal Processing, 46(1), 2014, 129-145.
[32] Bu, J., Law, S., Zhu, X., Innovative bridge condition assessment from dynamic response of a passing vehicle. Journal of Engineering Mechanics, 32(12), 2006, 1372-1379.
[33] Yang, Y., Chang, K., Extracting the bridge frequencies indirectly from a passing vehicle: Parametric study. Engineering Structures, 31(10), 2009, 2448-2459.
[34] Yang, Y., Li, Y., Chang, K., Using two connected vehicles to measure the frequencies of bridges with rough surface: a theoretical study. Acta Mechanica, 223(8), 2012, 1851-1861.
[35] Yang, Y., Chang, K., Li, Y., Filtering techniques for extracting bridge frequencies from a test vehicle moving over the bridge. Engineering Structures, 48, 2013, 353-362.
[36] Organisation, I.S., Mechanical vibration-road surface profiles-reporting of measured data, in ISO 8608:1995. 1995.
[37] Keenahan, J., et al., The use of a dynamic truck–trailer drive-by system to monitor bridge damping. Structural Health Monitoring, 13(2), 2014, 143-157.
[38] Clough, R.W., Penzien, J., Dynamics of structures. Berkeley: Computers & Structures. 1995, Inc.
[39] Tedesco, J.W., McDougal, W.G., Ross, C.A., Structural dynamics: theory and applications. 1999: Addison-Wesley Menlo Park, CA.